Job level potion only levels your job to 60, completes the jobquests up there, gives you a little bit of gear and gil (?), so you can start stormblood, if you have done the MSQ...

To jump right to the point of the MSQ who starts with stormblood you need the other type of jump potion, ithink they are calle "Tales of the Adventurerer Heavensward", which autocompletes all MSQ and sidequests neccessery for stormblood MSQ.